Ha! You type "P" for the symbol-- so he doesn't have his own Unicode codepoint?
The font may have an ambiguous license, but it appears that it was meant to be widely distributed to promote Prince. Is it available anywhere? I could make my own, but that wouldn't be the same.
No, he doesn't, and it's a crying shame. Contact your local Unicode consortium representative - If and ? deserve Unicode codepoints, the artist formerly known as Prince surely does too.
To propose this character to the UTC (Unicode Technical Committee) you'll need to include as many examples as possible showing the symbol used in running text. Physical objects and logos won't do; you need to show historical use of the symbol in running text (newspaper or magazine articles, books, liner notes, et cetera). Find examples, and we could make the proposal.
We've done it before on HN: